5 Spatial motion structures based
on the Bennett linkage
5.1 Introduction
Designing a large motion structure has different priorities from designing a
machine. There are two keys to a successful concept. First, to identify one
of a small number of robust and scalable building blocks made of known
mechanisms, and, second, to develop a way by which the building blocks
can be connected to form a large assembly while retaining the mobility of
each mechanism.
Motion structures developed over the past three decades are based mostly
on planar mechanisms, such as those introduced in Chapters 3 and 4. It is
rare to use truly three dimensional mechanisms. The reason is primarily
because the majority of structural engineers are less familiar with the three
dimensional mechanisms. In this chapter, we shall introduce types of motion
structures that are constructed by tessellation of the Bennett linkage.
The kinematics of Bennett linkage has been summarised in Chapter 2,
including its geometrical features and closure equations. As a spatial fourbar linkage, a typical Bennett linkage, Figure 5.1(a), consists of a closed
chain of four bars which span the shortest distance between two axes of
adjacent revolute joints. Each of the bars has lengths and twists identical
to those of the bar which is not directly connected to it. It therefore can be
represented schematically by a rectangle shown in Figure 5.1(b). Each side
of the rectangle corresponds to a link; at every corner where two links
meet is a revolute joint represented by a black dot. Twists of each link are
given alongside the respective bars. This simplified diagram will be used
throughout this chapter to avoid confusion in drawing real three dimensional assemblies. In the next section we shall use the Bennett linkage as
the building block to construct large motion structures.
5.2 Single- layer assembly of Bennett linkages
5.2.1 The layout
A layout of the motion structure is given in Figure 5.2(a) in which a
number of Bennett linkages represented by large rectangles similar to that
on the Bennett linkage
5.1 Introduction
Designing a large motion structure has different priorities from designing a
machine. There are two keys to a successful concept. First, to identify one
of a small number of robust and scalable building blocks made of known
mechanisms, and, second, to develop a way by which the building blocks
can be connected to form a large assembly while retaining the mobility of
each mechanism.
Motion structures developed over the past three decades are based mostly
on planar mechanisms, such as those introduced in Chapters 3 and 4. It is
rare to use truly three dimensional mechanisms. The reason is primarily
because the majority of structural engineers are less familiar with the three
dimensional mechanisms. In this chapter, we shall introduce types of motion
structures that are constructed by tessellation of the Bennett linkage.
The kinematics of Bennett linkage has been summarised in Chapter 2,
including its geometrical features and closure equations. As a spatial fourbar linkage, a typical Bennett linkage, Figure 5.1(a), consists of a closed
chain of four bars which span the shortest distance between two axes of
adjacent revolute joints. Each of the bars has lengths and twists identical
to those of the bar which is not directly connected to it. It therefore can be
represented schematically by a rectangle shown in Figure 5.1(b). Each side
of the rectangle corresponds to a link; at every corner where two links
meet is a revolute joint represented by a black dot. Twists of each link are
given alongside the respective bars. This simplified diagram will be used
throughout this chapter to avoid confusion in drawing real three dimensional assemblies. In the next section we shall use the Bennett linkage as
the building block to construct large motion structures.
5.2 Single- layer assembly of Bennett linkages
5.2.1 The layout
A layout of the motion structure is given in Figure 5.2(a) in which a
number of Bennett linkages represented by large rectangles similar to that